Assignment:
Part A : Two operators are measuring parts produced by two different machines. The team leader wants to test the difference between the sample means. Samples are taken in pairs and their differences are calculated. Please use the data in the table below to perform a hypothesis test at the 90%, 95%, and 99% confidence levels to determine if the mean of the two parts are different or not.
|
Machine 1 |
Machine 2 |
| 1 |
5.257 |
5.243 |
| 2 |
5.22 |
5.193 |
| 3 |
5.235 |
5.225 |
| 4 |
5.23 |
5.22 |
| 5 |
5.225 |
5.223 |
Part B : A vendor claim that the average weight of a shipment of n parts is 1.84. The customer randomly chooses 64 parts and finds that the sample has an average weight of 1.88. Suppose that the standard deviation of the population is known to be 0.03. Should the customer reject the lot? Assume 90%, 95%, 99% confidence intervals and comment on your answers.
Part C : An unusually high concentration of metals in drinking water can pose a health hazard. Ten pairs of data were taken measuring copper concentration (g/cm3) in the drinking water before and after using a water filter. Does the data suggest that the true average concentration in the drinking water before using the water filter exceeds that after using the water filter? Conduct the test at 1%, 5%, 10% significance levels.
| Before Using Water Filter |
After Using Water Filter |
| 0.430 |
0.415 |
| 0.266 |
0.238 |
| 0.567 |
0.390 |
| 0.531 |
0.410 |
| 0.707 |
0.605 |
| 0.716 |
0.609 |
| 0.651 |
0.632 |
| 0.589 |
0.523 |
| 0.469 |
0.411 |
| 0.723 |
0.612 |
Part D : A health researcher read that a 200-pound male can burn an average of 524 calories per hour playing tennis. 37 males were randomly selected and the mean number of calories burned per hour playing squash was 534.8 with a standard deviation of 45.9 calories. Do squash players burn more calories per hour than tennis players? Assume 90%, 95%, 99% confidence intervals and comment on your answers.